numerical and experimental investigations on heat … and experimental investigations on heat...

Numerical and Experimental Investigations on

Heat Transfer of Aluminum Microchannel Heat

Sinks with Different Channel Depths

Ngoctan Tran1, Yaw-Jen Chang1,, Jyh-tong Teng

1, and Thanhtrung Dang

2

1Department of Mechanical Engineering, Chung Yuan Christian University, Chung-Li, Taiwan

2Department of Heat and Refrigeration Technology, Ho Chi Minh City University of Technical Education, Hochiminh

City, Vietnam

Email: { ngoctantran73, jttengl} @gmail.com, [email protected], [email protected]

Abstract—In this study, heat transfer of aluminum

microchannel heat sinks (MCHs) was investigated with both

numerical and experimental methods. Five MCHs, each

with twelve channels, were designed with the channel width

of 500 μm, channel length of 33 mm, and channel depths

varying from 200 μm to 900 μm. Water was used as the

working fluid and Reynolds numbers, as independent

variables, were in the range of 100 to 1000. For all cases

done in this study, it is found that the heat transfer of

microchannel heat sinks was significantly affected by the

channel depth. At mass flow rate of 213 g/min, when the

channel depths increased from 200 μm to 900 μm, the heat

fluxes decreased from 31.8 W/cm2 to 15.8 W/cm2 and the

heat transfer rate increased from 113.3 W to 143.8 W. Good

agreement between numerical and experimental results was

achieved, with maximum percentage errors less than 6%.

Index Terms—microchannel heat sink, channel depth, heat

transfer rate, heat flux

I. INTRODUCTION

The needs of heat transfer devices for diverse

applications and the fascinating characteristics observed

in heat transfer field have attracted many scientists and

engineers to investigate the heat transfer and flow in

microchannel heat sinks. The inlet/outlet rectangular

shape was designed by Lelea [1], and six different types

of inlets/outlets were investigated numerically by Chein

and Chen [2]. Lee et al. [3] studied the effects of channels’

depth and width in rectangular copper microchannels

with Reynolds numbers ranging from 300 to 3,500. Dang

et al. [4] presented the investigations of heat transfer

phenomena of an aluminum microchannel heat sink, and

Tran et al. [5] presented studies on pressure drop and

performance index of an aluminum microchannel heat

sink. Wang et al. [6] presented an inverse geometric

optimization for nano-cooled microchannel heat sink. In

their research, water-based Al2O3 nanofluid with 1%

particle volume fraction was used as the working fluid.

Comparison of simulation data between CFD and

ANSYS Fluent regarding a direct bond copper for power

Manuscript received April 7, 2015; revised June 11, 2015.

electronics packaging was discussed by Yin et al. [7].

Their research emphasized the importance of entrance

effects on heat transfer and flow in the microchannel heat

sink. With the foundation of the previous studies, the

purpose of this study is to investigate experimentally and

numerically the effects of channel depths on the heat

transfer of aluminum microchannel heat sinks.

II. METHODOLOGY

A. Mathematical Model

Given by the CFD–ACE+ package, the governing

equations for this system consist of the incompressible

Navier-Stokes equations for the motion of fluid and the

energy equation for the transfer of heat [8]. The

incompressible Navier-Stokes equations can be expressed

by

𝜌𝜕𝐮

𝜕𝑡+ 𝜌(𝐮 ⋅ ∇)𝐮 = ∇ ⋅ [−𝑝𝐈 + 𝜇(∇𝐮 + (∇𝐮)𝑇)] + 𝐅 (1)

and

∇ ⋅ 𝐮 = 0 (2)

For steady-state conditions,𝜕𝐮𝜕𝑡⁄ = 0; the boundary

conditions of inlet flow are u = 0, v = 0, and w = 𝑤0 ;

the boundary conditions of outlet flow are 𝜇(∇𝐮 +(∇𝐮)𝑇)𝒏 = 0, and 𝑝 = 𝑝0; where µ is dynamic viscosity,

is density, u is velocity field, u is velocity in the x-

direction, v is velocity in the y-direction, w is velocity in

the z-direction, p is pressure, I is the unit diagonal matrix,

n is normal vector, and F is body force per unit volume

(F𝑥 = F𝑦 = F𝑧 = 0).

For the energy transport, no-slip conditions are

assumed for velocity and temperature at the walls; these

conditions are expressed by u𝑤𝑎𝑙𝑙 = 0 and T𝑤𝑎𝑙𝑙 =T𝑓𝑙𝑢𝑖𝑑 𝑎𝑡 𝑤𝑎𝑙𝑙 , respectively, where Twall is wall temperature.

The heat transfer equation for the energy transport by

the fluid is:

𝜌𝐶𝑝𝜕𝑇

𝜕𝑡+ ∇ ⋅ (−∇T) = 𝑄𝑖 − 𝜌𝐶𝑝𝒖 ⋅ ∇T. (3)

where 𝑄𝑖 is internal heat generation, T is temperature, 𝐶𝑝

is specific heat at constant pressure, and is thermal

conductivity. For steady-state conditions, 𝜕𝑇𝜕𝑡⁄ = 0; the

204© 2015 Int. J. Mech. Eng. Rob. Res.

International Journal of Mechanical Engineering and Robotics Research Vol. 4, No. 3, July 2015

doi: 10.18178/ijmerr.4.3.204-208

boundary condition of inlet flow is T = T0; the boundary

condition of outlet flow is convective flux, expressed by

𝐧 ⋅ (−∇T) = 0; the thermal boundary conditions of the

top wall and four side-walls of the microchannel heat sink

are assumed to be constant heat flux, expressed by

−𝐧 ⋅ (−∇T) = q0; and the thermal boundary condition

of the bottom wall is constant surface temperature

T = T𝑠. The energy balance equation for the

microchannel heat sinks is expressed by

𝑄 = 𝑚𝐶𝑝(𝑇𝑜 − 𝑇𝑖). (4)

where 𝑄 is heat transfer rate, m is mass flow rate, C𝑝 is

specific heat at constant pressure, Ti, and To are inlet and

outlet temperatures, respectively.

Heat flux is calculated by

𝑞 =Q

𝐴, or 𝑞 = 𝑘∆T𝑙𝑚 =

∆T𝑙𝑚

∑ 𝑅. (5)

The log mean temperature difference is calculated by

∆T𝑙𝑚 =∆T𝑚𝑎𝑥− ∆T𝑚𝑖𝑛

𝑙𝑛∆T𝑚𝑎𝑥∆T𝑚𝑖𝑛

, ∆T𝑚𝑎𝑥 = T𝑠 − T𝑖 ,

and ∆T𝑚𝑖𝑛 = T𝑠 − T𝑜 . (6)

where q is heat flux, A is heat transfer area, k is overall

heat transfer coefficient, ƩR overall thermal resistance, Ts

is surface temperature of the bottom wall.

Nusselt number is calculated by the following equation

[2].

Nu𝑅𝑒 =h𝑅𝑒Dℎ

𝑓, (7)

where Nu𝑅𝑒 is the Nusselt number achieved by varying

Reynolds number, hRe is the heat transfer coefficient of a

microchannel heat sink depending on the Reynolds

number, and f is the thermal conductivity of flow in the

channels.

B. Design and Set-up of the Test Facility

The experimental system used in this study was

designed with three major parts, including the test section,

syringe system, and overall testing loop, as shown in Fig.

1. For verifying the numerical results, two aluminum

substrates, with the same dimensions as shown in Fig. 2

except the differences in channel depths of 350 µm and

700 µm respectively for SD2 and SD4, were

manufactured as the test specimens for the experiments.

The substrates and its upper plates (top cover or PMMA

plate) which are showed in Fig. 3 were manufactured by

precision micromachining and bonded by UV (ultraviolet)

light process.

Figure. 1. Schematic diagram of the test loop for microchannel heat sinks

The substrates were designed with length of 48 mm,

width of 27 mm, and thickness of 1.8 mm; 12 channels in

each substrate were designed with a rectangular cross-

section having width Wc of 500 µm, length Lc of 33 mm,

distance between two adjacent microchannels of 500 µm,

and channel depths Dc being 200 µm, 350 µm, 500 µm,

700 µm, and 900 µm for five MCHs from SD1 to SD5,

respectively; two manifolds in each substrate were also

designed with a rectangular cross-section having width of

3 mm, length of 18 mm, and depth of 900 µm. The

substrates have the thermal conductivity of 237 W/(mK),

the specific heat of 904 J/(kgK), and the density of 2,700

kg/m3. The upper parts of the substrates were made of the

transparent PMMA (polymethyl methacrylate) with the

thickness of 10 mm, the thermal conductivity of 0.19

W/(mK), and the density of 1,420 kg/m3.

To operate the experimental system, the temperature of

the bottom wall of substrate was fixed at uniform

temperature of 50 oC, the room temperature was

controlled at around 25 to 26 oC, and the mass flow rate

of water was varied from 39 g/min to 213 g/min.

C. Numerical Simulation

In order to investigate the heat transfer of the twelve

microchannels inside the heat sinks, two manifolds, a

combination of inlet-outlet as well as overall the

microchannel heat sinks were simulated for numerical

analyses.

Numerical simulations of three-dimensional single-

phase heat transfer were performed by using CFD ACE+

software. Algorithm of this software is based on the finite

volume method. Five models have been built and 35 sets

of data have been simulated. The dimensions of

geometric configuration of the substrates are listed in

Table I and shown in Fig. 2. Water was used as the

working fluid. No internal heat generation was occurred,

resulting in Qi =0.

Figure. 2. Dimensions of the test section

III. RESULTS AND DISCUSSIONS

A. Numerical Results

In this study, the boundary conditions for simulations

were set as follows: the temperature of the inlet water

was fixed at 25.5 ºC, the mass flow rates (MFRs) were

varied from 39 g/min to 213 g/min, the bottom wall of the

substrate was fixed at a uniform temperature of 50ºC, and

the channel depths were varied from 200 µm to 900 µm



TABLE I. DIMENSIONS OF THE TEST SECTIONS

No.

Dimensions of manifolds

(mm)

Dimensions of

channels

(mm) (μm)

Lm Wm Tm Lc Wc Dc

SD1 18 3 0.9 33 500 200

SD2 18 3 0.9 33 500 350

SD3 18 3 0.9 33 500 500

SD4 18 3 0.9 33 500 700

SD5 18 3 0.9 33 500 900

Figure. 3. Photos of substrates, PMMA plate and microchannel heat sinks SD2 and SD4

Fig. 4 shows the isothermal profiles of MCH SD2 at

mass flow rate of 132 g/min. Results from Fig. 4 and such

profiles of other models under this study indicate that for

each microchannel heat sink, it always exists an

isothermal surface throughout the channels, the manifolds,

and the upper place.

Figure. 4. Isothermal surface profiles

Figure. 5. The No. 1 channel temperature of the five MCHs

Figure. 6. Heat flux versus MFR of the five MCHs

Figure. 7. Nusselt number versus Reynold number

Figure. 8. Comparison Num. and Exp. Results

Figure. 9. Comparison num. and exp. results

The comparison of numerical results for temperature of

the water moving in the No.1 channels of the five MCHs

(MCHs SD1-SD5) is presented in the Fig. 5. It is found

that the temperatures of water moving in channels with

deeper channel depth are higher than those having

shallower channel depth. It is noted that in this study, the

No.1 channel shown in Fig. 5 is the channel nearest to the

inlet of the MCH and the No. 12, the farthermost.

25

30

35

40

0 3 6 9 12 15 18 21 24 27 30 33

Tem

per

atu

re,

oC

Length of channels, mm

SD1

SD2

SD3

SD4

SD5

0

10

20

30

40

50

35 65 95 125 155 185 215

Hea

t fl

ux, W

/cm

2

Mass flow rate, g/min

SD1

SD2

SD3

SD4

0

2

4

6

8

10

12

0 200 400 600 800 1000

Nu

selt

nu

mb

er

Reynolds number

SD1

SD2

SD3

SD4

0

20

40

60

80

100

120

140

160

35 65 95 125 155 185 215

Hea

t tr

an

sfer r

ate

, W


SD4-Exp. result

SD4-Num. result

SD2-Exp. result

0

1

2

3

35 65 95 125 155 185 215

Hea

t tr

an

sfer c

oeff

icie

nt,

W/c

m2K


SD4-Exp. result

SD4-Num. result

SD2-Exp. Result

SD2-Num. result

Substrate

Channel

s

Manifold

s PMMA

plate

Microchannel heat sink SD2

Inlet Outlet

Microchannel heat sink SD4



Fig. 6 shows a comparison of numerical results for

heat fluxes of the five MCHs. The comparison shows that

the heat fluxes increased from 15.8 W/cm2 to 31.8 W/cm

2

when the channel depths decreased from 900 μm to 200

μm. In addition, the maximum heat flux of 31.8 W/cm2 is

obtained for the MCH SD1 at a MFR of 213 g/min.

Results obtained for the Nusselt number versus the

Reynolds number for the MCHs from SD1 to SD5 in the

laminar developing flow region are shown in Fig. 7. The

results show that the Nusselt number increased when the

Reynolds number increased or the channel depth

decreased.

B. Experimental Results

The experiments were performed in a room maintained

at the temperature around 25 to 26 ºC. Deionized water

was used as the working fluid, the boundary conditions

were discussed in the previous section, and the MFR was

varied from 39 g/min to 213 g/min. Apparatuses used for

the experiments are listed as follows:

Thermocouple wires: model PT-100, made by

Omega

Pumps: model PU-2087, made by JASCO

Differential pressure transducer: model PMP4110,

made by GE Druck

Thermoelectric heater: model TEC1-241.10, made

by Championtech Technology

A comparison of numerical and experimental data for

heat transfer rate of MCHs SD2 and SD4 is presented in

Fig. 8. The results show that the heat transfer rate

increased when the MFR increased, and good agreements

between numerical and experimental results are achieved

with maximum percentage error of 6 %. A comparison of

numerical and experimental results for heat transfer

coefficient of MCHs SD2 and SD4 is presented in Fig. 9.

The results show that the heat transfer coefficient

increased when the MFR increased or the channel depth

decreased. Good agreement between numerical and

experimental results is achieved, with maximum

percentage error of 5.8 %.

IV. CONCLUSIONS

In this study, the effects of channel depth to heat

transfer of five microchannel systems have been studied

using both numerical and experimental methods. For the

two cases being investigated experimentally in this study

(with the channel depths of 350µm and 700 µm), good

agreement between numerical and experimental results

was achieved, with maximum percentage errors to be less

than 6%. A maximum heat flux of 31.8 W/cm2 was

achieved for the MCH SD1 (with the channel depth of

200 µm) at the MFR of 213 g/min. Besides, the

maximum heat transfer rate of 143.8 W was achieved for

the MCH SD5 (with the channel depth of 900µm) at the

MFR of 213 g/min. As far as the impact of the channel

depth on the behaviors of heat transfer associated with the

microchannel heat sink systems is concerned, when the

channel depths increased from 200 μm to 900 μm, the

heat fluxes decreased from 31.8 W/cm2 to 15.8 W/cm

2 at

the mass flow rate of 213 g/min.

Furthermore, the overall microchannel heat sink,

including the channels, manifolds, substrate, inlet-outlet,

and the top cover has been simulated by using the CFD –

ACE+ package.

ACKNOWLEDGMENT

The supports of this work by (1) the project (Project

Nos. NSC 99-2221-E-033-025 and NSC 100-2221-E-

033-065) sponsored by National Science Council of the

Republic of China in Taiwan and (2) the project (under

Grant No. CYCU-98-CR-ME) sponsored by the specific

research fields at Chung Yuan Christian University,

Taiwan, are deeply appreciated.

REFERENCES

[1] D. Lelea, “Effects of inlet geometry on heat transfer and fluid flow

of tangential micro-heat sink,” Int. J. Heat Mass Transf., vol. 53,

pp. 3562-3569, April 2010. [2] R. Chein and J. Chen, “Numerical study of the inlet/outlet

arrangement effect on microchannel heat sink performance,”

International Journal of Thermal Sciences, vol. 48, pp. 1627-1638, January 2009.

[3] P. S. Lee, S. V. Garimella, and D. Liu, “International Journal of

Thermal SciencesInvestigation of heat transfer in rectangular microchannels,” Int. J. Heat Mass Transf., vol. 48, pp. 1688-1704,

March 2005.

[4] T. T. Dang, N. T Tran, and J. T. Teng, “Numerical and experimental investigations on heat transfer phenomena of an

aluminium microchannel heat sink,” Appl. Mech. Mater., vol. 145,

pp. 129-133, 2012.

[5] N. T Tran, T. T Dang, C. P Zhang, and J. T Teng, “Studies on

pressure drop and performance index of an aluminum

microchannel heat sink,” in Proc. Int. Symp. Computer, Consumer and Control, Taichung, 2012, pp. 252-257.

[6] X. D. Wang, B. An, L. Lin, and D. J. Lee, “Inverse geometric

optimization for geometry of nano fluid –cooled microchannel heat sink,” Appl. Therm. Eng., vol. 55, pp. 87, March 2013.

[7] S. Yin, K. J. Tseng, and J. Zhao, “Design of AlN-based micro-

channel heat sink in direct bond copper for power electronics packaging,” Appl. Therm. Eng., vol. 52, pp. 120-129, Nov. 2013.

[8] Advanced CFD -ACE+ Version 2008.2.8, Documentation, 2008.

Ngoctan Tran received his B.S. degree in the

Department of Heat and Refrigeration

Technology, Ho Chi Minh City University of Technical Education (HCMUTE), Vietnam in

2009 and received his M.S. degree in

Department of Mechanical Engineering, Chung

Yuan Christian University, Taiwan in 2012. He

employed part–time for P.Dussmann Vietnam

Co., Ltd as a Supervisor of Engineering from 2008 to 2009, employed full–time for

P.Dussmann Vietnam Co., Ltd as a Manager of Laundry Factory from

2009 to 2010, and employed for Darling Electronic–refrigerator Co., Ltd as a technical director in 2010. Presently, he is a Ph.D. student at

Department of Mechanical Engineering, Chung Yuan Christian

University, Taiwan. He interested in studying on nano/microscale heat transfer, industrial refrigeration and air conditioning, electronic and

control system engineering, and Bio- MEMS.

Yaw-Jen Chang received the M.S. degrees in

both Department of Mechanical Engineering

and Department of Systems Science and Mathematics from Washington University, St.

Louis, and the Ph.D. degree in Systems and Control Engineering from Case Western

Reserve University. He is an Associate

Professor of Mechanical Engineering at Chung Yuan Christian University, Taiwan,

R.O.C. His research interests focus on Bio-



MEMS, advanced process control for semiconductor manufacturing, and intelligent control.

Thanhtrung Dang, PhD, APE, is an Associate Professor in the Department of Heat

and Refrigeration Technology and the Vice

Dean of the Faculty of Vehicle and Energy Engineering, Hochiminh City University of

Technology and Education (HCMUTE),

Vietnam. He received his BS and MS in the Department of Thermal Technology at

Vietnam National University Hochiminh city

– Hochiminh city University of Technology (HCMUT), PhD in the Department of Mechanical Engineering, Chung

Yuan Christian University (CYCU), Taiwan. His main research interests

are nano/microscale heat transfer, energy and sustainable development, industrial refrigeration and air conditioning, and energy economics.

Jyh-tong Teng, PhD, PE, is a professor in the Department of Mechanical Engineering and

the Senior consultant of the Office of

International Affairs at Chung Yuan Christian University (CYCU), Taiwan. He is also the

principal investigator of an international

education enhancement program sponsored by the Ministry of Education, Republic of China.

He received his BS in Mechanical

Engineering from Montana State University, MS and PhD in Mechanical Engineering from UC Berkeley. His

research areas include thermo-fluidic analyses of compartment fires and

smokes, nuclear safety, thermo-fluidics of microchannels, and thermal management of electronic devices.



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